The problem asks whether we can construct a model of set theory without the Axiom of Choice in which ultrafilters on the natural numbers exist but none of them are P-points, and simultaneously the standard chain condition tools used in forcing, which normally rely on Choice, break down in ways that prevent us from controlling which ultrafilters survive. This sits at the intersection of two active research threads: the recent simplified proof that P-points may be absent, and the emerging study of how chain conditions behave in choiceless set theory. We want to understand whether these two phenomena can coexist in a single coherent mathematical universe, and what constraints one places on the other.